Mathematical analysis of contact inhbition model in tumour growth

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13462
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Meiji University
• Principal Investigator: Mimura Masayasu 明治大学, 研究・知財戦略機構, 研究推進員(客員研究員) (50068128)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 摂食抑制 / 細胞増殖モデル / 進行波解 / 自由境界問題

Outline of Final Research Achievements

When cells contact with either external boundaries or other cell group, they stop growing as well as migrating, that is, contact inhibition. Under the assumption where cells lose contact inhibition, we consider the situation in which some normal cells convert abnormal ones. Then it is expected the possibility of unlimited growing of abnormal cells. This may suggest the initiation of cancer cells. In this research, we propose a cell-growth model including the property of contact inhibition between normal and abnormal cells and represent the growth-velocity of abnormal cells by velocity of traveling wave (TW) solutions of the model. The result shows that there exist different types of TW solutions such as segregated TWs, overlapping TWs, and partially overlapping TWs with characteristic velocities, depending on the values of growth rates and interaction between two cells.

Free Research Field

数物系科学、現象数理学